Why do I so rarely hear a MAJOR 3rd in a bassline?

Its all about overall note choice.

Like I said earlier, you can dial in how "blue" or minor your bassline sounds. If you crank the dial all the way to the left and play pure minor pentatonic with minor 3rds, you get one sound. But if you add 2s and 6s or b 6s, with that minor 3rd, you start sounding like Van Morrisons Moondance. So its 6s as well as 3s and 7s that shape the sound.

Playing major 3rds is compatible with the guitarist or other playing minor pentatonic if they play at least an octave above you. Then the sound is interesting rather than dissonant (you are making maj 7s rather than min 2s).
Along with this, you should decide whether you stick to b7s or use 6s which are a different sound with the maj 3. Btw, some older blues players are very particular on use/avoid 6ths.

A useful exercise is to play a bassline that totally avoids the 3rd and 6th. Think pentatonic without the 3rd (root , 5 b7, 2nd and 4ths ok). You can even do this on walking blues bass lines but avoiding the maj or minor 3rd is a hard habit because we have been trained to outline the harmony with 3s and 7s. If you are doing a new song with new people , its useful to avoid the 3rd early in the song until you get a clear idea which feel they want.

I am taking DB lessons from a classically trained symphony guy right now and comparing music theory ideas have been mutually amusing and enlightening. So he is teaching me about baroque cadences and i am showing him bebop 3/7s.

Edit: PS, if the song chord structure and melody is major pentatonic, you probably should be emphasizing major 3s and 6s.
 
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